In advanced civilizations the period loosely called Alexandrian is usually associated with flexible morals, perfunctory religion, populist standards and cosmopolitan tastes, feminism, exotic cults, and the rapid turnover of high and low fads—in short, a falling away (which is all that decadence means) from the strictness of traditional rules, embodied in character and inforced from within. — Jacques Barzun

Sleeping Beauty

Some researchers are going to put you to sleep. During the two days that your sleep will last, they will briefly wake you up either once or twice, depending on the toss of a fair coin (Heads: once; Tails: twice). After each waking, they will put you to back to sleep with a drug that makes you forget that waking. When you are first awakened, to what degree ought you believe that the outcome of the coin toss is Heads?

Related

3 Responses

I don’t get why “thirders” think “halvers” do not have probability on their side. Will you explain this please? I’m very right brained. I can also see why someone might say that it is equally probably that both views are correct, but . . . . HELP!

Also, is the next digit, 1221? That seems one possible correct response; i.e., simply a quantifying of the previous digit.

I don’t know what to think of this puzzle, myself. I think there’s a reasonable argument for either position, and it seems possible to Dutch book either position, so it’s hard to know what rationality demands here. Some people have strong intuitions; I lean toward being a “thirder,” but it’s a weak leaning.

On the third math puzzle: there are of course infinitely many sequences that start with 1, 11, 21, 1211, but the next number of the sequence I had in mind is 111221.